In this study, circular disk model and cylinder theory for two dimension (2D) and three dimension (3D), respectively, have been used to determine residual stresses in three-phase representative volume element. The representative volume element is consisting of three phases: carbon fiber, carbon nanotubes, and polymer matrix, that carbon fiber is reinforced by carbon nanotube using electrophoresis method. Initially, the residual stresses analysis of two-phase representative volume element has been implemented. The two-phase representative volume element has been divided to carbon fiber and matrix phases with different volume fractions. In the three-phase representative volume element, although the volume fraction of carbon fiber is constant and equal to 60%, the volume fractions of carbon nanotubes for various cases are different as 0%, 1%, 2%, 3%, 4%, and 5%. Also, there are two different methods to reinforce the fiber according to different coefficients of thermal expansion of the carbon fiber and carbon nanotube in two longitudinal and transverse directions; carbon nanotubes are placed on carbon fiber either parallel or around it like a ring. Subsequently, finite element method and circular disk model have been used for analyzing micromechanic of the residual stresses for 2D and then the results of stress invariant obtained by the finite element method have been compared with the circular disk model. Moreover, for 3D model, the finite element method and cylinder theory have been utilized for micromechanical analysis of the residual stresses and the results of stress invariant obtained by them, have been compared with each other. Results of the finite element method and analytical model have good agreement in 2D and 3D models.
Numerical Investigation on Mechanical Behaviour of Closed-cell Aluminium Foams Using a Representative Volume Element Method
